As the purpose of the question was to update the answers under the older one, I will try to maintain here an updated answer on the programs that I was able to test, discussing the solutions that have been proposed.
I will leave aside for now DVDShrink in Wine.
For a while k9copy, which many have recommended in the past, and which, as already stated under this question, is considered the real DVDShrink alternative for Ubuntu, was not supported. But, as the initial project is now inactive, there is a new developer that supports a k9copy-reloaded version. Deb packages can be found HERE. To add a PPA - look HERE; in one line:
sudo add-apt-repository && apt-get update && apt-get install k9copy
I have installed without any problems the latest deb posted there - the Jessie version - in a Kubuntu 15.04-development branch. It has added only 13 new dependencies.
In Ubuntu Unity and any other non-KDE desktops it will come with a lot more KDE dependencies. But that is the problem with many other KDE applications that at some point may be needed for a specific purpose. If your purpose is to backup DVS-s the way DVDShrink does in Windows, then having some KDE dependencies is not such a bad deal.
k9copy looks like a real alternative and for now the only answer to the question.
Considering other tools that were mentioned on askubuntu and that I was able to test at some point:
DVD9to5 (dvd95) - I have tested it by making a backup of two video-dvds as iso files. (They were both larger than 5 GB and maybe protected). There is an option to keep the menus, which I suppose means the structure of the original dvd.
But the iso files were not playable in VLC.
And I think I know why. In fact DVD95 cannot select and backup more than one track each time (a confirmation of this here).
While it may work ok with dvd movies that have only one such track (have to test that yet) the ones that have multiple tracks will put a big problem. These are dvds with more than a single movie. When backing up a dvd with multiple tracks the original menus will be lost because they relate to the other files that will not be copied. Also, subtitles are not usable in this way, and also scrolling does not work. The separate vob files would be playable separately.
In a such case the good part is that you have a better quality of the main video than in the case all the dvd image would have been there (like DVDSrink can do). I noticed in one case that the main video that was selected kept its original size, and all "shrinking" of the image was done only by removing the other tracks. It is not the same image in this way. But if that is not a problem for you (you do not need menus and subtitles) you may use a simple command
dvdbackup -F (source for this here: How do I make an ISO copy of a DVD movie?) and in this way get only the main feature which might very well be smaller than 4.7GB
- DVD95 may be an alternative only in the case of dvds with a single track.
Handbrake - can convert dvd video to MKV and to mp4: maybe a good solution to convert (have not tested it yet), but not to 'shrink' dvd images,
so, Handbrake is not a DVDShrink alternative.
xDVDShrink (also .deb) - Does not work on all dvd sources (encrypted etc). The dvds tested above were not even accessed, so I tested with 4.7 dvd movie without protection.
No support for subtitles is seems (also mentioned here), one single video title and one single audio channel selectable it looks.
I had made also these settings:
that were not followed. No .iso file was to be found on the desktop or elsewhere. But nor the /tmp files had been deleted as set, so I was able to test those. The full dvd files were found in
/tmp/mydvd/BUILD/, but they can be played with VLC and SMPlayer just as ordinary video files, without the original dvd structure of menus. The most severe problem is the absence of subtitles (funny in my case as I was testing with a Japanese movie.)
Therefore: xDVDShrink is NOT an alternative.
I will try to keep this post up to date.